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Design and Operability of an Energy Integrated Distillation Column
Design and Operability of an . Energy Integrated Distillation Column: Torben Mf:1nsted Schmidt, Arne Koggersbf:11 and Sten Bay Jf:1rgensen.
Department of Chemical Engineering, Technical University of Denmark. DK .. 2800 Lyngby, Denmark. --
Abstract Operability issues are investigated on an energy integrated distillation column. The distillation column separates a nearly binary mixture. The energy integration is achieved using an indirect heat pump between the column condenser and the reboiler. The design aim of the integrated is system to enable operation of the distillation column over its entire operating window, through manipulation of theheatpumpvariables. An additional aim is to provide the operator with a set of standard distillation column actuators, for controlling the distillation column asa conventional distillation column. This secondary aim is attempted achieved, through selection of the control structure of the heat pump. Both simulation and experimental results illustrate areas within the possible operating window where potential operability problems remain dependent upon the selected control configuration. A very large part of the totally possible operating window may be covered by using just one heat pump control struCture. However multivariable . control avoids singularity of the multiloop structure.
Introduction The purpose of designing integrated process plants is to make better use of raw materials and to construct more . energy efficient plants. In integrated plants additional .dynamic and static interactions exist. these interactions may render the plants more difficult to operate. Interactions may depend significantly upon both operating conditions and upon the chosen control configuration. Several authors have addressed the issue of how design Of integrated plants affects theoperalional aspects. Heat exchanger network problems (HEN) have 'been widely used to illustrate how heat 'integration can limit the operation space. Most investigations have focused upon static aspects e.g. Saboo · and Morari (1982), . Calandrias and SlephanopouJous (1986). The purpose of this paper is 10 investigate the ,intera:ciion effects of an indirecl heatpump upon the operability properties of a distillation column. anti to cilttem,'P"L
The article is structured as follows. In section 2 a short discussion on operability related issues is given. The energy integrated distiUationcolumn is described in section 3. Stability and operability issues of the heat integrated distillation column arc iltlurcsscdin section 4.h is shown that the degree offreedom for control of a distillation column operalingat full reflux is two when the distillation batch is given. The variables chosen 10 · describe lheoperalion window for the distillation column are discussed. and finally it is argued why the energy . integr:llion operability problems, can be investigated by investigating the system whe.n the distillation column is operated at full reflux. In sectionS a detailed dynamic nonlinear model the system is described and [he main assumptions for the model are given. Steady state relations between the variables of the distillation column and the heat pump actuators are given in section 6. In section 7 controllability properties of the system are investigated using line:lr models derived from the t1clailctl nonlinear model In section 8experiOlental results are given, :lnd finally the conclusions are . . reached.
or
31
2. Operability issues of integrated plants. Operability of a plant may be viewed as a combination o(stability,ftexibility, .switchability and controllability properties. The three latter properties have a relatively dear frequency separation as depicted below, Per-kins
(1989). •
·The fte~bility of a plant considers the ability of a plant to operate at different steady states.
•
..The switchability of a plan considers the ability of a plant .to be moved from one steady state ~ operatingpointto another. Thus the switchability "-depends upon the ability to follow low frequency · setpoints changes. The switchability also involve ~-:thestartup and shut down of the process.
.•
The controllabiliryof a plant considers the ability of a plant to reject high frequency disturbances.
The flexibility issues depends mainly on the structure of the process while both the swichability and controllability issues also depend upon the selected control structure. Compared to a conventional distillation column, a distiUation column heated by an 'indirect heatpump is expected to have additional operability problems, because of the interactions caused by the connection between the condenser and the reboiler through theheatpump. A qualitative discussion concerning the poteniial operability problems in a distillation column heated hy an indirect heatpump is given in section 4
Figure 1. Simplified flowslreet of the refrigerant circuit the heatpllmp.
energy to an external cooling circuit. The liquified refrigerant is throttled through a valve, before the column condenser,thus dosing the circuit of the refrigerant in the indirect heat pump. In order to control the energy supply and removal from the heatpump, the heat pump is equipped with two actuators: A throule V
3.PI3'l1t Description. When an indirect .heatpump is used in connection with a distillation column. the energy removed from the ··condenser is reused in the rcb(likr through the circulation of a refri~t:rant in a closed circuit. A simplified flowsheet the refrigerant circuit in the heat integr
ot·
32
the inlet lo the compressor, byheat exchange with (h~ high press~r~ liquid refrigerant, thus $upe(heating the wpour.thlS IS done. (0 ensure that liquidterrigerant does not reach the compressor. . .The energy balance of the distillation cOlumn is (hus determined by the two 'heatpump pressures. The dosed loop refrigerant circuit of .theheatpump is .shoWn in a PresSure -Enthalpi (H,P) diagram in FJgUre 2, in order to illustrate the relation between the two pressures in the beatpump and the energy supply to theQlluaut. kentropic ,rompresOOrl, isenthalpic ·throttIing,isobarlc evaporation and condensation are assumed. A more .detailed description of the plant is given in Hallageret al (1986).
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When the process is operated at full reflux tbe system
f'
,
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configured such that the accumulator level is controlled by 'the reflux rate. the high pressure is controlled byCV8 and the 'low pressure 'b yCV9.
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.has·<%! l~mber of'flow leii.doonlml~e~ U,ese/.oops aloe
I
'......
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:
400.0
Entholpi (KJ/KG) Figure 2. The refrigerant cUcltit ;11 011 £nUla/pi-Pressure diagram. A: Condenser• .B Qnd E: HeatexcJlanger. C Reboi/er. D: Aftercondellser.
4. Stability and operabHityof the plant This paper mainly addresses the controllability issues
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of the. plant. However, first however.a brief discussion is given or problems in a distillation column heated bv . an indirect heatpump, which do not exist in ~ conventional distiilation column.
The consequence of supplying the energy with an indirect heat pump to the distillation column is that the heat supply and heat removal are closelv linked, this will riot be.the case in a conventional di~tillation column. This coupling can limit the possible operation window of the distillation column. Safety limits on the pressures in the he3tpump \...,113Iso limit lhe possible operalion window .of the distillation column in a complicated way.
Stability: the energy part of the plant is open loop unstable, i.e with fixed control valve in the heatpump, the plant3ctS like a pure integrator. This can be seen from (he · following argumentation. If the system is operated :It a steady state and the control valves are fixed, a disturbance which gives an increasing high pressure will result in botb .3 higher column pressure and a higher vapour flow, Through the column condenser . these will both increase th~ healpump low ·pressure and (he compressor inlet pressure. This increased inlet presslH"e would increase the high pressure further. thus positive feedback is established . . Using idealized conditions this . effect is equivalent to an integration process. The integrating effect can be direct Iv visualized by noting that a the energy input · to th~ integrated process under infinite reflux is fLxcd tbrou{!h (he power input to the compressor and the energy output .is fLxed through (he position of CV9 which determines the cooling power. 'If (he powcr input and output differ, th~intt!grated proccss will integwte this imbalance. This pole at zero ' is easily stabilized by controlling either the high pressure or the compressor inlet pressure in the heat pump.
Switchability: Necessary conditions for the operation .of the distillation ,c.olumn. are th
33
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The Vapour~liquid equilibrium in the distillation cohimn arecalclIlated by original UNIFAC.
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The thermodynamic properties of the refrigerant in the beatpump are .calculated by the SRK equation of state.
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Constant tray efficiency of 60 ·% on an trays.
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Constant beat of \'3pOri7.ation throughout the . column.
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Heat transfer coefficients are Iin6lr in the refrigerant flow.
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Quasi stationary ideal vapOur phase.
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~~~--~~,~o~~~·~~~~~~~~~~,~~~~
P'esSUf'e ct toptroy (kpO)
Figure 3. Steady Slate .relatiOll .between d.e heatp.ln'p pressures. die c:oIumtr pressure and llle ~'apour flow rate. 77leheatpump pressures are dlangedill Sleps of 10 kPa. n,e nJarlced operatiOlI points areim'eStigated further.
A more detaileddesaiption oC the assumptions in modelling the energy integrated distillation column, the estimation of parameters; the solution method used for solving the DAE and a comparison of simulation results with experimental results is given in Hansen et al. (1991).
is
prochlcing, since the couplings caused by the heatpumpare only directly arrecting the energy balance of the distillation column, i.e. the column pressure and the internal flows, but not the eXternal flow.. The reason for investigating the distillation column system under full reflux is simplicity, The number of degrees offreedom for control is reduced from five to only two, when there are no p rod UClS and the batch is given. When the distillation column is operated under full reOux the column preSsure and the vapOr flowrate is just one example of a variable pair which fully specify the operation of the distillation column. i
On vector form the model can be wriuen as.
· (1)
dr.,
-= F(xlrr."u) dl . -
(2)
where x., is a vector of the dynamic variables, Xl is a vector~f the algebraic variables, u is a vector containing both the control variables and disturbances to the process and G and Fare nonlinear vector functions.
5. Modelling of the energy integraledplant A detailed dynamic simulation program for the energy ;integrated distillation column plant has been developed. The nonlinear modd of the · process consist's of a set of coupled ordinary differential and algebraic equations (DAE) . The differential equations originate from first principles modelling of Citc::rgy and mass balances in the distillation column and in the heatpu~mp, while the algebraic .equations describe the thermodynamic equilibrium and hydraulic relationship in the distillation column and the therillodynamic equilibrium in (he heatpump. Parameters in the model which (;ould not be obtained from literature were estimated from experimental data.
6. Steady state operation of plant In figure 3the calculated steady state relationship for the distillation column pressure and vapour Oow are shown for different high and 10\" pressures in the heatpump. For a constant high (or low) pressure it can be seen from the figure how the column pressure and the vapour flow changes for changes in the low (or high) pressure. St~tic nonlinearities in (he model are dtarly seen. A change in the selpoint for the high and low pressure will have different effects upon the colurrin pressure and .the vapor flow rate dependent upon the actual operation potn!. At high column pressure a change in the heatpump high pressure will have a larger effect upon {he distillation column variables (han :it low column pressure. It is also seen
The main assumptions of the nonlinear model are the following:
34
Table J
Where
difJeroll ()perotioll conditions
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which Qre further
Un-estigoted.
. Case
Phim
Plow
Nn1
.1300.
600. .
10
1250,
600.
10
03
1250.
550.
10
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11:50.
500.
Os
11.50.
450.
06
1200.
500.
10
071
1200.
550.
10
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. .-dF dll
If Yi is a measurement oC a dynamic variable cOntained in x"the i'th row or ciS a. row with one element cqu;ltoone a~d the rest equal 'to zero. If Yi is a Measurement of an algebraic variable'Yi is found as a linear combination ' oC the ' dynam ic variables, ihe i'ih roW of C is thus a row oC Cc, where: .
10 16
LaplacetransCorming the linearised state space model . eq (3) and (4), an input output model is formulated: Y(s) = C(ls-A)-IB-U(s)
In order to reveal the dynamic effects of different physical elements on ' the distillation column control propeiti~, theSVD and the RGA are calculated (or different linear models~ ' The linear models are . calculated for three different cases~ The first case is at different operation condi(io~s chosen in order to cover the operating window as in Figure 3 as shown in Tabel I. The second case is Jor different tunings of the accumulator level controller, and the third case is for different heat transfer areas (or coefficients) in the heat exchanger between the high and low pressure refrigerant. In Figure 4 and Figure 5 the upper and lower singular values and the input and output alignments are shown for the different operation conditions shown in Table 1. Within the entire operation region the accumulator level luning is fixed and the controllers for the high and low pressure by the two c\.)ntrol \"alv~sin the hc:atpump are tuned ,·ery lightly. From the SVO gains in Figure 4 and Sit is seen that both the upper and lower singular values have essentially lhe same time constants for all the operating points, independent of the: number of cylinders active in the heat pump. From the input alignment in Figure 4 and 5. it is seen that the upper singular \-alue is most affected by the low pressure selpoint allow frequency, while at higher frequency the upper singular value is mainly affected by the high pressuresetpoinL From the output alignment in Figure .~ and 5. it is seen that at lo\~' frequency the upper singular value only aCrectsthe column pressure, where at high frequency the vapour \low rate is only affected by lhe .lower singular value.
that at high vapour flow rate the effect ola (:bange in one oftbe beatpumppressures will have a larger effect than at low vaporOow rate. A singularity can be cbse~ed w.hcnkcepm.g high pressure constant and changing the low pressure in the heat pump. When the low pressure in the healpump is small (top . part of figure 3) an increasing low pressure will give an increasing column pressure but a decreasing vapour flow rate,whiJeJofiarge low pressure in the hc.. tpump (botlOmparl of figure 3) ani~crea$ing low pressure will cause a decrease in both (he distillation column pressure and in the vapour flow ratc.
me
7. Controllability properties .of theplanl Th~ controllability propenies orihc plant are investigated by singuiar value decomposition (SVD) Lau . et all (1986),Grosdidicr ' (19<)0) and by investigation of . (he relative gal 11 .. rray (RGA) Skogestadet all (1987) of input-output models. Linearising the dynamicnonlinear model eq (I) and (2) around .a n operating point a state space model is obtained. The variables arc scaled. such that the outputs \'aria(ions~re of cqual.inagnilutle.
(3)
(4)
35
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r reqvency
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/0"
(rod sec)
Figure 5.
Figure 4.
0.60
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Freq\Jency (rOd/sec)
)0"
Frequency (rod/ sec)
Figure 7.
Figure 6.
III Figure 4, 5, 6 alld 7, lillear models for the differelll operatioll poillls slwlVI/ ill Table J are illvestigated. III Figwe 4 olld 5 the tipper alld lower sillglllar "allles, the relati,'c gai" of tire illPIII olld the outpllt oligll/1/ems 10 the upper singlllar "olue ore showlI.11/ figure 6 and i the J,I elemcnls a/the RGA arc showlI. Illll" plots the first illp/{( is the setpoil1t to tile high pressure il/ tfle IIeotpump (77le Iow pressure setpoilll iSlhe second) al/d Ihe,'opOllr flow rate is the first Olllplll (the colllmll pressure is IIIe secolld).
36
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t
--01 . - - 02 . ---- DJ ' ---- 004
.
.....-01
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~~
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--. _
I
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~~
Figure 9. /'101 oJ tllel,l demt:ni of the RGA for oJ the QccunuIIQ(o,.le\re/ controUer. ·17,e first input is tile setpoint Jor tlrehigIJ presSllre, and lhe first output is .ti,e l'CpollF flow rote.
/"
difJereilt IlInings
,
,',' .:.,.l
....<~c;.. . _......~
plots are shown for operation point 06 (in the middle of the operation window in figure 3) with different lunings of the accumulator . level controller. The accumulator 'level controller ,was tuned bv the IMC rules given by Chien et al1 (1990). A PlO controller was tuned to h41ve "the follo\\,iig dosed loop time c~)nSlants: 01: 15 see; 02: 60 sec (originalluning), 03: 120 sec and 04: 240 sec. The SVO plot shQwsthat when the controller is de tuned, both singular values and the input and output alignment are · all affected similarly. Also the RGA plot shows that interaction between the two SISO loops is most dependent upon the tuning of accumulator level loop at low frequency. The heatexchaO(!e bet\veen the refriger-Clnt at low . pressure and at high pressure served to superheal the rdrigcrant, in ordert\) guarantee that condensation of rcfrigenint in the compressordoes not occur. Stalically this docs not cause problems, but dynamically the hcatcxchanger could introduce serious 'couplings beIW~en(heheatpunip , and the distillation column, which couldarfecled the .c ontrol properties.The effect of the.: heatcxchanger was investigatedQY changing the h\!allransfer area, ilOd investigate the SVD and RGA plols. 11 was secn , that the healexch:lIIger had very s01;,1I effect on the interactions in the process,both whc:n the process was investigated as a multivariable and as a O1uhiloop problem. The reason Cor (his limilCd iniluence is probably that (he coupling is ~\lmpktcly thermic and the heat t-ransCerred in this h\!alexchangc.:r ' ~s insignificant compared to the h':;lItrans(cr in thc rehOilcrantl condenser.
......- 01 ---- 02 .
--..; DJ - '- 04
10'"
~~
FreQu,eney (rod/sec)
)O~
frequency (rod sec)
Figure 8. Singular value plot Jor differefll timings of IIle, Qccumulatot level cOlllrollcr.17,c inpulistlte .IJigl!
-pressure sel]Joim and the oittpllt tIJel'opour /lOIV ralc.
-
The SVO plots in Figure 4 ano 5 show that as a mullivariabeI control problem there does nol seem (0 be large differences between the different operation points, but within the frequency range of intercsl foi control significant interactions exist. In Figure 6 and 7 the 1,1 element of the RGA is shown for the operation conditions given in Tablel. In figure 3 is was ()bs.erved that the steady "state gain from the low pressure setpoint lothe column pressure changes ·sign intne lower part of the operation ,Vindo\V; This sign change is also. seen for operaling point 02 .ind 010, from the RGA plot. From the RGA plot is also seen that if the . distillation column is to be controlled by dosingSISO loops to the heatpump aClU.llors, the high pressim.: setpoint :should be used to controllhe vapour Ilow anti the low pressure selpoin! to conttoltlie column presSure. ,From the RGA plot it is also seen that when conrrolling the process by SISOloops, the interactions in the process will depend more of the operating conditions, lhan when the process is coni rolled as a multivariable process, ' In Figure 8 singular value plots .tnd in Figure 9 RGA
37
-
-
2.25
"U
:(f)
'C
'(I)
'U
c o
'0
nooding 'limit (Zu.iderweg. 1982) Weeping limit (Zuiderweg.1982) xxxxx EX120.391 . D/\/\/\/\ EX190391 oOClooEX240791 OEGOE) EX181291 . . ,.. "' .. ' ,I' .'1: EX060292 -
1.7'5
-
..
..c. .......... 'E1.25 ""'-'
o\
Q \
··\...0.75 .:J
'. 0
0
0
---
Q.
o
>. 0.2'5
C-
30
50
0
I
I
q \
I
- -
I
I
\ I ~
ID '0' .'
O
90
70
110
.Column pressure (kPo) Figure lO
Figure la. Experimelltal illvesligaJiollso/ the steady sla.terclOliollsllip belweellthe lIeolpump pressllres,tliecolunllI pressure and vapour f!olvrate. III l/le,t!tperimelll Oil the 18//2 1991, first the high pressure was kept constalltwhile the lowpressure was iilcreased, thell the Iow pressurel~'as k~p( COlIs(alll alldthelzigh pressure WaS incteased. /11 the experimellf Ofl the 6/2 1992 tOllseClIl;l'e ,hallces Were made ill (he Jziglr aild Iow presSllres. .
8. Experimental results In order 10 reveal operability properties oflheenergy integrated distillation . ,column at the Technical University 'o f Denmark a series of experiments havc been carried out. The experimental results presented here are all from full rellux cxperiments with batches oC 'approximately the same size and the same composition. The main 'purpose of the experiments \vere to investigate the static relation between the . heatpump ' vari;bles and the distillation column variablC!$ over a large part of lheoperation window. As ' .discussed in section 3 this relationship ' can be investigated using fullreOu.'(C!xperiments. Then! ' are several adv~ntages of oper~lling the distillation column under full ·retllL,( compared to prod.uction, in addilion to the simplicity asml!nlioncd in section J. The . 6ldditional advantages are lirsdy that the time constant atfull reflux is much smaller Ihail at production. \vhich
means that lime used .for experiments can reduced wilhout Jossofinformation. Secondly several potential sources for disturbances to the column are removed. There is however ' one dra\vback, the removal of .products in the lOp and in the bottom can be used for disturbance rejectiqn under production. Disturbances under full reflux in the distillation column has to be removed by theheatpump, such disturbance rejection may be difficult due to . the direct coupling to the column. . . In Figure 10 Steady state relations between the distillation column and the heatpump variables are shown for selected experiments in a column pressure versus vaPOUr ,nO\" diagram. In the experiments on the 18/12 1991 and the 6/2 1992 the relation between separate changes in the high and low pressures in the heal pump upon the
38
"Towards integration design ,and control: Use of Crequcncy-dependenttools for controllability analysiS"'. Presented at PSE '91, MontebeUo Canada, Aug 5-9. .
,d istiUationcolumnvariables were investigated. In the first. experiments the Jowprcssurc in the heatpump wasdcqeased three limes by 25 kPa and then the high pressure in the hc:atpump wasincre:lsed three limes by 75 kPa. ,I n.the second experiment Changes in first the high;tnd then the Jow pressure where performed. for a number of different operations points. As also observed in figure 3, the experiments show that at very low vapour flow. a change in the low pressure has a very small effect upon the column pressures, but the sign change ~ich:was obsetVed with the simulation program. was not s.een in theSe experiments, this might be caliscd by operation . at too . high vapour now rate and due to 'beginning weeping the vapour flow rate \vas not loWered further. From the e:
Hallager L; Toftegard B.; Clement K and Jorgensett S. B. 1986. •A Distillation Plan with a indirect Heat Pump for Experimental Studies of Operation Form, Dynamics and Control-. DYCORD'86, Bournemouth, England.
Haoscn A. K;Jensen N. and Jergensen S. B. 1991. ·Dynamic modelling and simulationofa heatintegrated distillation column with sidestream'". Presented at European simulation multiconference,COpenhagen. Denmark. June 17-19. Chicn I. Land Fruenhauf P. S. 1990. "Consider IMC luning lO . improve .controller performance"'. Chem. Eng. Progress. No. 10 pp 33-41. lau h. Alvarez J; and Jensen K .F. 1985. ·Synthesis of Control Structures by Singular Value Analysis: Dynamic Measures . of Sensiti~ity and Interaction-. AIChE J. 31(3). 3 pp 427-439. Grosdidierp.
. Operability properties of an energy integrated distillation column h:l\'e beeninvestigatcd. lritegr:llion of an indirect heatpump with a disliUationcolumn invokes loss of stabiIityoflheiritegraledplanl, due an integratingefTect of the energy balanc~; ihis aspect .is however easily handled using control and thus does not impair operability. It is shown thatmullivariable control ofthe heat pump is advanlageous ·{o multiloop control in order to avoid · singularilY of muhiloop configuralionin specific . regions of (he distill;.lIion columnoperaling window.
to
"AnalySis of interaction direction
Skogeslad S. and Morari M. 1987. -Implications of large RGA elements on control performance'~ Ind . Eng. Chem. Res, 26~ pp 2323-2330. Zuiderweg F. J. 1982. -Sieve Trays. A view on the stale of art". Chcm Eng Sci. 37. pp 1441~14(j4.
Literature Saboo A. K and Morari M. 19R.:t. -Design of Rcsilil:nt ProcesSing Plan Is •VI. Some new results on HI!3t Exchagger NetworkSynlhcsis-. Chcm . Eng. Sci. 39 pp
579.
1990~
with the singular value decomposition"'. Comp. Chem. Engng. 14. pp 687-698. .
.
Calandranis J . and Stephanopoulos G. 1986. -Structural OperabililY Analysis of Hcal Exc11:aIH!.cr networks". Chem. Eng. Res. Dcs. 6~ pp 3-17·364. Perkins J. D. 1989. -lnlcraCliillls between process design and .. process conlrol". IFAC symposium DYCORp + '89. MaaSlrict, The Netherlands. Aug 2123. p349-357. Skogestad S.: Hovd M. and LundSlrum P. 1991.
39
Department of Chemical Engineering, Technical University of Denmark. DK .. 2800 Lyngby, Denmark. --
Abstract Operability issues are investigated on an energy integrated distillation column. The distillation column separates a nearly binary mixture. The energy integration is achieved using an indirect heat pump between the column condenser and the reboiler. The design aim of the integrated is system to enable operation of the distillation column over its entire operating window, through manipulation of theheatpumpvariables. An additional aim is to provide the operator with a set of standard distillation column actuators, for controlling the distillation column asa conventional distillation column. This secondary aim is attempted achieved, through selection of the control structure of the heat pump. Both simulation and experimental results illustrate areas within the possible operating window where potential operability problems remain dependent upon the selected control configuration. A very large part of the totally possible operating window may be covered by using just one heat pump control struCture. However multivariable . control avoids singularity of the multiloop structure.
Introduction The purpose of designing integrated process plants is to make better use of raw materials and to construct more . energy efficient plants. In integrated plants additional .dynamic and static interactions exist. these interactions may render the plants more difficult to operate. Interactions may depend significantly upon both operating conditions and upon the chosen control configuration. Several authors have addressed the issue of how design Of integrated plants affects theoperalional aspects. Heat exchanger network problems (HEN) have 'been widely used to illustrate how heat 'integration can limit the operation space. Most investigations have focused upon static aspects e.g. Saboo · and Morari (1982), . Calandrias and SlephanopouJous (1986). The purpose of this paper is 10 investigate the ,intera:ciion effects of an indirecl heatpump upon the operability properties of a distillation column. anti to cilttem,'P"L
The article is structured as follows. In section 2 a short discussion on operability related issues is given. The energy integrated distiUationcolumn is described in section 3. Stability and operability issues of the heat integrated distillation column arc iltlurcsscdin section 4.h is shown that the degree offreedom for control of a distillation column operalingat full reflux is two when the distillation batch is given. The variables chosen 10 · describe lheoperalion window for the distillation column are discussed. and finally it is argued why the energy . integr:llion operability problems, can be investigated by investigating the system whe.n the distillation column is operated at full reflux. In sectionS a detailed dynamic nonlinear model the system is described and [he main assumptions for the model are given. Steady state relations between the variables of the distillation column and the heat pump actuators are given in section 6. In section 7 controllability properties of the system are investigated using line:lr models derived from the t1clailctl nonlinear model In section 8experiOlental results are given, :lnd finally the conclusions are . . reached.
or
31
2. Operability issues of integrated plants. Operability of a plant may be viewed as a combination o(stability,ftexibility, .switchability and controllability properties. The three latter properties have a relatively dear frequency separation as depicted below, Per-kins
(1989). •
·The fte~bility of a plant considers the ability of a plant to operate at different steady states.
•
..The switchability of a plan considers the ability of a plant .to be moved from one steady state ~ operatingpointto another. Thus the switchability "-depends upon the ability to follow low frequency · setpoints changes. The switchability also involve ~-:thestartup and shut down of the process.
.•
The controllabiliryof a plant considers the ability of a plant to reject high frequency disturbances.
The flexibility issues depends mainly on the structure of the process while both the swichability and controllability issues also depend upon the selected control structure. Compared to a conventional distillation column, a distiUation column heated by an 'indirect heatpump is expected to have additional operability problems, because of the interactions caused by the connection between the condenser and the reboiler through theheatpump. A qualitative discussion concerning the poteniial operability problems in a distillation column heated hy an indirect heatpump is given in section 4
Figure 1. Simplified flowslreet of the refrigerant circuit the heatpllmp.
energy to an external cooling circuit. The liquified refrigerant is throttled through a valve, before the column condenser,thus dosing the circuit of the refrigerant in the indirect heat pump. In order to control the energy supply and removal from the heatpump, the heat pump is equipped with two actuators: A throule V
3.PI3'l1t Description. When an indirect .heatpump is used in connection with a distillation column. the energy removed from the ··condenser is reused in the rcb(likr through the circulation of a refri~t:rant in a closed circuit. A simplified flowsheet the refrigerant circuit in the heat integr
ot·
32
the inlet lo the compressor, byheat exchange with (h~ high press~r~ liquid refrigerant, thus $upe(heating the wpour.thlS IS done. (0 ensure that liquidterrigerant does not reach the compressor. . .The energy balance of the distillation cOlumn is (hus determined by the two 'heatpump pressures. The dosed loop refrigerant circuit of .theheatpump is .shoWn in a PresSure -Enthalpi (H,P) diagram in FJgUre 2, in order to illustrate the relation between the two pressures in the beatpump and the energy supply to theQlluaut. kentropic ,rompresOOrl, isenthalpic ·throttIing,isobarlc evaporation and condensation are assumed. A more .detailed description of the plant is given in Hallageret al (1986).
...t··--,-, ....
I
••••
I
I.
p....
,
I
A
I I
. i e
I
I I
i
.
I
' 0:
f
'f
...''-':"1
. 300.0
,
/'
I
, , , ~oo.o
:
le,
I
When the process is operated at full reflux tbe system
f'
,
•••1
,,
configured such that the accumulator level is controlled by 'the reflux rate. the high pressure is controlled byCV8 and the 'low pressure 'b yCV9.
: '
-f I
..- ,
E
.has·<%! l~mber of'flow leii.doonlml~e~ U,ese/.oops aloe
I
'......
,
I
I
I
I:
I
:
400.0
Entholpi (KJ/KG) Figure 2. The refrigerant cUcltit ;11 011 £nUla/pi-Pressure diagram. A: Condenser• .B Qnd E: HeatexcJlanger. C Reboi/er. D: Aftercondellser.
4. Stability and operabHityof the plant This paper mainly addresses the controllability issues
Fle:
of the. plant. However, first however.a brief discussion is given or problems in a distillation column heated bv . an indirect heatpump, which do not exist in ~ conventional distiilation column.
The consequence of supplying the energy with an indirect heat pump to the distillation column is that the heat supply and heat removal are closelv linked, this will riot be.the case in a conventional di~tillation column. This coupling can limit the possible operation window of the distillation column. Safety limits on the pressures in the he3tpump \...,113Iso limit lhe possible operalion window .of the distillation column in a complicated way.
Stability: the energy part of the plant is open loop unstable, i.e with fixed control valve in the heatpump, the plant3ctS like a pure integrator. This can be seen from (he · following argumentation. If the system is operated :It a steady state and the control valves are fixed, a disturbance which gives an increasing high pressure will result in botb .3 higher column pressure and a higher vapour flow, Through the column condenser . these will both increase th~ healpump low ·pressure and (he compressor inlet pressure. This increased inlet presslH"e would increase the high pressure further. thus positive feedback is established . . Using idealized conditions this . effect is equivalent to an integration process. The integrating effect can be direct Iv visualized by noting that a the energy input · to th~ integrated process under infinite reflux is fLxcd tbrou{!h (he power input to the compressor and the energy output .is fLxed through (he position of CV9 which determines the cooling power. 'If (he powcr input and output differ, th~intt!grated proccss will integwte this imbalance. This pole at zero ' is easily stabilized by controlling either the high pressure or the compressor inlet pressure in the heat pump.
Switchability: Necessary conditions for the operation .of the distillation ,c.olumn. are th
33
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..
,
.p
Ngt>
I.io
Z .'.. ...... .9')
--i..
.E t.20
-1200
. .. .-.. .. P""" .500 :':- :'-:';5;:-~\' :-.: •.••• ... . . . ... .. . . . .."..: :1'/ ..........:, .. .." .. .. . .
,.s
~..
"
..
.
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..
~.
.
a: o.~
•
The Vapour~liquid equilibrium in the distillation cohimn arecalclIlated by original UNIFAC.
•
The thermodynamic properties of the refrigerant in the beatpump are .calculated by the SRK equation of state.
•
Constant tray efficiency of 60 ·% on an trays.
•
Constant beat of \'3pOri7.ation throughout the . column.
•
Heat transfer coefficients are Iin6lr in the refrigerant flow.
...... ... . .. .
..
. . . "..,.3-..
",G.eO.
. 4/ .
Quasi stationary ideal vapOur phase.
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....
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-.
!~.
..
..
... •
. .
• • • ,. GJ-
.
~~~--~~,~o~~~·~~~~~~~~~~,~~~~
P'esSUf'e ct toptroy (kpO)
Figure 3. Steady Slate .relatiOll .between d.e heatp.ln'p pressures. die c:oIumtr pressure and llle ~'apour flow rate. 77leheatpump pressures are dlangedill Sleps of 10 kPa. n,e nJarlced operatiOlI points areim'eStigated further.
A more detaileddesaiption oC the assumptions in modelling the energy integrated distillation column, the estimation of parameters; the solution method used for solving the DAE and a comparison of simulation results with experimental results is given in Hansen et al. (1991).
is
prochlcing, since the couplings caused by the heatpumpare only directly arrecting the energy balance of the distillation column, i.e. the column pressure and the internal flows, but not the eXternal flow.. The reason for investigating the distillation column system under full reflux is simplicity, The number of degrees offreedom for control is reduced from five to only two, when there are no p rod UClS and the batch is given. When the distillation column is operated under full reOux the column preSsure and the vapOr flowrate is just one example of a variable pair which fully specify the operation of the distillation column. i
On vector form the model can be wriuen as.
· (1)
dr.,
-= F(xlrr."u) dl . -
(2)
where x., is a vector of the dynamic variables, Xl is a vector~f the algebraic variables, u is a vector containing both the control variables and disturbances to the process and G and Fare nonlinear vector functions.
5. Modelling of the energy integraledplant A detailed dynamic simulation program for the energy ;integrated distillation column plant has been developed. The nonlinear modd of the · process consist's of a set of coupled ordinary differential and algebraic equations (DAE) . The differential equations originate from first principles modelling of Citc::rgy and mass balances in the distillation column and in the heatpu~mp, while the algebraic .equations describe the thermodynamic equilibrium and hydraulic relationship in the distillation column and the therillodynamic equilibrium in (he heatpump. Parameters in the model which (;ould not be obtained from literature were estimated from experimental data.
6. Steady state operation of plant In figure 3the calculated steady state relationship for the distillation column pressure and vapour Oow are shown for different high and 10\" pressures in the heatpump. For a constant high (or low) pressure it can be seen from the figure how the column pressure and the vapour flow changes for changes in the low (or high) pressure. St~tic nonlinearities in (he model are dtarly seen. A change in the selpoint for the high and low pressure will have different effects upon the colurrin pressure and .the vapor flow rate dependent upon the actual operation potn!. At high column pressure a change in the heatpump high pressure will have a larger effect upon {he distillation column variables (han :it low column pressure. It is also seen
The main assumptions of the nonlinear model are the following:
34
Table J
Where
difJeroll ()perotioll conditions
Vie
which Qre further
Un-estigoted.
. Case
Phim
Plow
Nn1
.1300.
600. .
10
1250,
600.
10
03
1250.
550.
10
O~
11:50.
500.
Os
11.50.
450.
06
1200.
500.
10
071
1200.
550.
10
Os
ll00~
450;
16
09
1300.
550.
10
0)0
11.50.
540.
10
0,
°2
"
..
.
.. .
B.
. .-dF dll
If Yi is a measurement oC a dynamic variable cOntained in x"the i'th row or ciS a. row with one element cqu;ltoone a~d the rest equal 'to zero. If Yi is a Measurement of an algebraic variable'Yi is found as a linear combination ' oC the ' dynam ic variables, ihe i'ih roW of C is thus a row oC Cc, where: .
10 16
LaplacetransCorming the linearised state space model . eq (3) and (4), an input output model is formulated: Y(s) = C(ls-A)-IB-U(s)
In order to reveal the dynamic effects of different physical elements on ' the distillation column control propeiti~, theSVD and the RGA are calculated (or different linear models~ ' The linear models are . calculated for three different cases~ The first case is at different operation condi(io~s chosen in order to cover the operating window as in Figure 3 as shown in Tabel I. The second case is Jor different tunings of the accumulator level controller, and the third case is for different heat transfer areas (or coefficients) in the heat exchanger between the high and low pressure refrigerant. In Figure 4 and Figure 5 the upper and lower singular values and the input and output alignments are shown for the different operation conditions shown in Table 1. Within the entire operation region the accumulator level luning is fixed and the controllers for the high and low pressure by the two c\.)ntrol \"alv~sin the hc:atpump are tuned ,·ery lightly. From the SVO gains in Figure 4 and Sit is seen that both the upper and lower singular values have essentially lhe same time constants for all the operating points, independent of the: number of cylinders active in the heat pump. From the input alignment in Figure 4 and 5. it is seen that the upper singular \-alue is most affected by the low pressure selpoint allow frequency, while at higher frequency the upper singular value is mainly affected by the high pressuresetpoinL From the output alignment in Figure .~ and 5. it is seen that at lo\~' frequency the upper singular value only aCrectsthe column pressure, where at high frequency the vapour \low rate is only affected by lhe .lower singular value.
that at high vapour flow rate the effect ola (:bange in one oftbe beatpumppressures will have a larger effect than at low vaporOow rate. A singularity can be cbse~ed w.hcnkcepm.g high pressure constant and changing the low pressure in the heat pump. When the low pressure in the healpump is small (top . part of figure 3) an increasing low pressure will give an increasing column pressure but a decreasing vapour flow rate,whiJeJofiarge low pressure in the hc.. tpump (botlOmparl of figure 3) ani~crea$ing low pressure will cause a decrease in both (he distillation column pressure and in the vapour flow ratc.
me
7. Controllability properties .of theplanl Th~ controllability propenies orihc plant are investigated by singuiar value decomposition (SVD) Lau . et all (1986),Grosdidicr ' (19<)0) and by investigation of . (he relative gal 11 .. rray (RGA) Skogestadet all (1987) of input-output models. Linearising the dynamicnonlinear model eq (I) and (2) around .a n operating point a state space model is obtained. The variables arc scaled. such that the outputs \'aria(ions~re of cqual.inagnilutle.
(3)
(4)
35
-06 --07 ---- 08 ---- 09 - '-010
--01
--02
----03
---- a.
---0$
1
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.5
0.00
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-
- ,- ' 06 ---- '07
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--- as
t,
- -- a. 05
-
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\\ \'~
- - 09 - '010
+-...................................,..--.-............,..;,...:.;,,.,...-..........................-l
0.00
10'"
10"
r reqvency
...
/0"
(rod sec)
Figure 5.
Figure 4.
0.60
T--...-........~~--.,.----.................,
~---...................
-"-01
r,
---- 02
- - - a,}
- - o· - - o~
---- 06
--
~
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E cv
,C
~
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Cl)
-
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10 -,
---- - - - -0.00
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__ -
__ /
/
Q) -0.20
""
10-·
10"
Freq\Jency (rOd/sec)
)0"
Frequency (rod/ sec)
Figure 7.
Figure 6.
III Figure 4, 5, 6 alld 7, lillear models for the differelll operatioll poillls slwlVI/ ill Table J are illvestigated. III Figwe 4 olld 5 the tipper alld lower sillglllar "allles, the relati,'c gai" of tire illPIII olld the outpllt oligll/1/ems 10 the upper singlllar "olue ore showlI.11/ figure 6 and i the J,I elemcnls a/the RGA arc showlI. Illll" plots the first illp/{( is the setpoil1t to tile high pressure il/ tfle IIeotpump (77le Iow pressure setpoilll iSlhe second) al/d Ihe,'opOllr flow rate is the first Olllplll (the colllmll pressure is IIIe secolld).
36
-r----......,. . . . . ,
0 .&0 ....-......-....-..............-;.......- - - -..................
t
--01 . - - 02 . ---- DJ ' ---- 004
.
.....-01
.• ';;-- D2 '
- - - DJ - - 04
'0"" . .........~~~~__--~
--DAO~-.-----~~~--~--
~~
'~'---~~~~-r--~~~~~=---------~ ~,-:- , , ,. I --01 I I: I ---- 07 - - - OJ ' I ,~l --04 I j I
--. _
I
I' .:. : •
~~
Figure 9. /'101 oJ tllel,l demt:ni of the RGA for oJ the QccunuIIQ(o,.le\re/ controUer. ·17,e first input is tile setpoint Jor tlrehigIJ presSllre, and lhe first output is .ti,e l'CpollF flow rote.
/"
difJereilt IlInings
,
,',' .:.,.l
....<~c;.. . _......~
plots are shown for operation point 06 (in the middle of the operation window in figure 3) with different lunings of the accumulator . level controller. The accumulator 'level controller ,was tuned bv the IMC rules given by Chien et al1 (1990). A PlO controller was tuned to h41ve "the follo\\,iig dosed loop time c~)nSlants: 01: 15 see; 02: 60 sec (originalluning), 03: 120 sec and 04: 240 sec. The SVO plot shQwsthat when the controller is de tuned, both singular values and the input and output alignment are · all affected similarly. Also the RGA plot shows that interaction between the two SISO loops is most dependent upon the tuning of accumulator level loop at low frequency. The heatexchaO(!e bet\veen the refriger-Clnt at low . pressure and at high pressure served to superheal the rdrigcrant, in ordert\) guarantee that condensation of rcfrigenint in the compressordoes not occur. Stalically this docs not cause problems, but dynamically the hcatcxchanger could introduce serious 'couplings beIW~en(heheatpunip , and the distillation column, which couldarfecled the .c ontrol properties.The effect of the.: heatcxchanger was investigatedQY changing the h\!allransfer area, ilOd investigate the SVD and RGA plols. 11 was secn , that the healexch:lIIger had very s01;,1I effect on the interactions in the process,both whc:n the process was investigated as a multivariable and as a O1uhiloop problem. The reason Cor (his limilCd iniluence is probably that (he coupling is ~\lmpktcly thermic and the heat t-ransCerred in this h\!alexchangc.:r ' ~s insignificant compared to the h':;lItrans(cr in thc rehOilcrantl condenser.
......- 01 ---- 02 .
--..; DJ - '- 04
10'"
~~
FreQu,eney (rod/sec)
)O~
frequency (rod sec)
Figure 8. Singular value plot Jor differefll timings of IIle, Qccumulatot level cOlllrollcr.17,c inpulistlte .IJigl!
-pressure sel]Joim and the oittpllt tIJel'opour /lOIV ralc.
-
The SVO plots in Figure 4 ano 5 show that as a mullivariabeI control problem there does nol seem (0 be large differences between the different operation points, but within the frequency range of intercsl foi control significant interactions exist. In Figure 6 and 7 the 1,1 element of the RGA is shown for the operation conditions given in Tablel. In figure 3 is was ()bs.erved that the steady "state gain from the low pressure setpoint lothe column pressure changes ·sign intne lower part of the operation ,Vindo\V; This sign change is also. seen for operaling point 02 .ind 010, from the RGA plot. From the RGA plot is also seen that if the . distillation column is to be controlled by dosingSISO loops to the heatpump aClU.llors, the high pressim.: setpoint :should be used to controllhe vapour Ilow anti the low pressure selpoin! to conttoltlie column presSure. ,From the RGA plot it is also seen that when conrrolling the process by SISOloops, the interactions in the process will depend more of the operating conditions, lhan when the process is coni rolled as a multivariable process, ' In Figure 8 singular value plots .tnd in Figure 9 RGA
37
-
-
2.25
"U
:(f)
'C
'(I)
'U
c o
'0
nooding 'limit (Zu.iderweg. 1982) Weeping limit (Zuiderweg.1982) xxxxx EX120.391 . D/\/\/\/\ EX190391 oOClooEX240791 OEGOE) EX181291 . . ,.. "' .. ' ,I' .'1: EX060292 -
1.7'5
-
..
..c. .......... 'E1.25 ""'-'
o\
Q \
··\...0.75 .:J
'. 0
0
0
---
Q.
o
>. 0.2'5
C-
30
50
0
I
I
q \
I
- -
I
I
\ I ~
ID '0' .'
O
90
70
110
.Column pressure (kPo) Figure lO
Figure la. Experimelltal illvesligaJiollso/ the steady sla.terclOliollsllip belweellthe lIeolpump pressllres,tliecolunllI pressure and vapour f!olvrate. III l/le,t!tperimelll Oil the 18//2 1991, first the high pressure was kept constalltwhile the lowpressure was iilcreased, thell the Iow pressurel~'as k~p( COlIs(alll alldthelzigh pressure WaS incteased. /11 the experimellf Ofl the 6/2 1992 tOllseClIl;l'e ,hallces Were made ill (he Jziglr aild Iow presSllres. .
8. Experimental results In order 10 reveal operability properties oflheenergy integrated distillation . ,column at the Technical University 'o f Denmark a series of experiments havc been carried out. The experimental results presented here are all from full rellux cxperiments with batches oC 'approximately the same size and the same composition. The main 'purpose of the experiments \vere to investigate the static relation between the . heatpump ' vari;bles and the distillation column variablC!$ over a large part of lheoperation window. As ' .discussed in section 3 this relationship ' can be investigated using fullreOu.'(C!xperiments. Then! ' are several adv~ntages of oper~lling the distillation column under full ·retllL,( compared to prod.uction, in addilion to the simplicity asml!nlioncd in section J. The . 6ldditional advantages are lirsdy that the time constant atfull reflux is much smaller Ihail at production. \vhich
means that lime used .for experiments can reduced wilhout Jossofinformation. Secondly several potential sources for disturbances to the column are removed. There is however ' one dra\vback, the removal of .products in the lOp and in the bottom can be used for disturbance rejectiqn under production. Disturbances under full reflux in the distillation column has to be removed by theheatpump, such disturbance rejection may be difficult due to . the direct coupling to the column. . . In Figure 10 Steady state relations between the distillation column and the heatpump variables are shown for selected experiments in a column pressure versus vaPOUr ,nO\" diagram. In the experiments on the 18/12 1991 and the 6/2 1992 the relation between separate changes in the high and low pressures in the heal pump upon the
38
"Towards integration design ,and control: Use of Crequcncy-dependenttools for controllability analysiS"'. Presented at PSE '91, MontebeUo Canada, Aug 5-9. .
,d istiUationcolumnvariables were investigated. In the first. experiments the Jowprcssurc in the heatpump wasdcqeased three limes by 25 kPa and then the high pressure in the hc:atpump wasincre:lsed three limes by 75 kPa. ,I n.the second experiment Changes in first the high;tnd then the Jow pressure where performed. for a number of different operations points. As also observed in figure 3, the experiments show that at very low vapour flow. a change in the low pressure has a very small effect upon the column pressures, but the sign change ~ich:was obsetVed with the simulation program. was not s.een in theSe experiments, this might be caliscd by operation . at too . high vapour now rate and due to 'beginning weeping the vapour flow rate \vas not loWered further. From the e:
Hallager L; Toftegard B.; Clement K and Jorgensett S. B. 1986. •A Distillation Plan with a indirect Heat Pump for Experimental Studies of Operation Form, Dynamics and Control-. DYCORD'86, Bournemouth, England.
Haoscn A. K;Jensen N. and Jergensen S. B. 1991. ·Dynamic modelling and simulationofa heatintegrated distillation column with sidestream'". Presented at European simulation multiconference,COpenhagen. Denmark. June 17-19. Chicn I. Land Fruenhauf P. S. 1990. "Consider IMC luning lO . improve .controller performance"'. Chem. Eng. Progress. No. 10 pp 33-41. lau h. Alvarez J; and Jensen K .F. 1985. ·Synthesis of Control Structures by Singular Value Analysis: Dynamic Measures . of Sensiti~ity and Interaction-. AIChE J. 31(3). 3 pp 427-439. Grosdidierp.
. Operability properties of an energy integrated distillation column h:l\'e beeninvestigatcd. lritegr:llion of an indirect heatpump with a disliUationcolumn invokes loss of stabiIityoflheiritegraledplanl, due an integratingefTect of the energy balanc~; ihis aspect .is however easily handled using control and thus does not impair operability. It is shown thatmullivariable control ofthe heat pump is advanlageous ·{o multiloop control in order to avoid · singularilY of muhiloop configuralionin specific . regions of (he distill;.lIion columnoperaling window.
to
"AnalySis of interaction direction
Skogeslad S. and Morari M. 1987. -Implications of large RGA elements on control performance'~ Ind . Eng. Chem. Res, 26~ pp 2323-2330. Zuiderweg F. J. 1982. -Sieve Trays. A view on the stale of art". Chcm Eng Sci. 37. pp 1441~14(j4.
Literature Saboo A. K and Morari M. 19R.:t. -Design of Rcsilil:nt ProcesSing Plan Is •VI. Some new results on HI!3t Exchagger NetworkSynlhcsis-. Chcm . Eng. Sci. 39 pp
579.
1990~
with the singular value decomposition"'. Comp. Chem. Engng. 14. pp 687-698. .
.
Calandranis J . and Stephanopoulos G. 1986. -Structural OperabililY Analysis of Hcal Exc11:aIH!.cr networks". Chem. Eng. Res. Dcs. 6~ pp 3-17·364. Perkins J. D. 1989. -lnlcraCliillls between process design and .. process conlrol". IFAC symposium DYCORp + '89. MaaSlrict, The Netherlands. Aug 2123. p349-357. Skogestad S.: Hovd M. and LundSlrum P. 1991.
39